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Singular levels and topological invariants of Morse Bott integrable systems on surfaces. (English) Zbl 1352.37129

Summary: We classify up to homeomorphisms closed curves and eights of saddle points on orientable closed surfaces. This classification is applied to Morse Bott foliations and Morse Bott integrable systems allowing us to define a complete invariant. We state also a realization Theorem based in two transformations and one generator (the foliation of the sphere with two centers).

MSC:

37E35 Flows on surfaces
57R30 Foliations in differential topology; geometric theory
57R70 Critical points and critical submanifolds in differential topology
58K65 Topological invariants on manifolds
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